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Unformatted text preview: ECE 307: Electricity and Magnetism Spring 2010 Instructor: J.D. Williams, Assistant Professor Electrical and Computer Engineering University of Alabama in Huntsville 406 Optics Building, Huntsville, Al 35899 Phone: (256) 8242898, email: [email protected] Course material posted on UAH Angel course management website Textbook: M.N.O. Sadiku, Elements of Electromagnetics 4 th ed . Oxford University Press, 2007. Optional Reading: H.M. Shey, Div Grad Curl and all that: an informal text on vector calculus, 4 th ed . Norton Press, 2005. All figures taken from primary textbook unless otherwise cited. 8/11/2010 2 Chapter 8: Magnetic Forces Materials and Devices • Topics Covered – Forces Due to Magnetic Fields – Magnetic Torque and Moment – A Magnetic Dipole – Magnetization in Materials – Classification of Magnetic Materials – Magnetic Boundary Conditions – Inductors and Inductances – Magnetic Energy – Magnetic Circuits – Forces on Magnetic Materials • Homework: All figures taken from primary textbook unless otherwise cited. Lorentz Force Law • Recall that the force on a charged particle is simply F =q E • If the particle moves however, then an additional force is imposed from the charge displacement of velocity, u , quantified by the magnetic field, B . The combined force is called the Lorentz Law: • Recall from Newton’s Law that • The kinetic energy of a charged particle in an electric field is therefore 8/11/2010 3 ) ( B u E q F × + = dt u d m a m B u E q F = = × + = ) ( 2 2 1 ) ( u m KE dt m qE u dt m qE u dt m qE u dt u d m E q F z z y y x x = = = = = = ∫ ∫ ∫ dt u l dt l d u i i ∫ = = The location of the particle can also be found as Forces Due to a Magnetic Field • Recall that the force on a charged particle is simply F =q E • If the particle moves however, then an additional force is imposed from the charge displacement of velocity, u , quantified by the magnetic field, B . The combined force is called the Lorentz Law: • Recall from Newton’s Law that • The kinetic energy of a charged particle in an magnetic field is therefore 8/11/2010 4 ) ( B u E q F × + = dt u d m a m B u E q F = = × + = ) ( 2 2 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( u m KE dt m B v B v q dt m B v q u dt m B v B v q dt m B v q u dt m B v B v q dt m B v q u dt u d m B v q F x y y x z z x z z x y y y z z y x x = − = × = − − = × = − = × = = × = ∫ ∫ ∫ ∫ ∫ ∫ dt l d u = The location of the particle can also be found as For B , u , and a in orthogonal directions, One can deduce a coordinate system in which ) ( ˆ ) ( ) ( 3 3 2 1 2 2 1 1 = × = = × = = = × = ∫ ∫ ∫ ∫ ∫ dt m B v q u u u dt m B v q u dt v dt m B v q dt m B v q u ω m B q = ω Cyclotron Resonance Frequency dt u l i i ∫ = Velocity of a Particle with no...
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This note was uploaded on 12/14/2011 for the course EE 307 taught by Professor Williams during the Spring '10 term at University of Alabama  Huntsville.
 Spring '10
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